W.E. Boyce, R.C. DiPrima, Elementer Diferansiyel Denklemler ve Sınır Değer Problemleri, Çev., M. Uğuz, Ç. Ürtiş, 10. Baskıdan Çeviri, Palme Yayıncılık, 2016.
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction; Classification of Differential Equations, Linear Equations; Method of Integrating Factors; Variation of Parameters
Lecture and applications
2. Week
Separable Differential Equations; Homogeneous Equations; Exact Equations and Integrating Factors; The Existence and Uniqueness Theorem
Lecture and applications
3. Week
Second-Order Linear Differential Equations; Homogeneous Equations with Constant Coefficients, Solutions of Linear Homogeneous Equations; the Wronskian
Lecture and applications
4. Week
Complex Roots of the Characteristic Equation; Repeated Roots; Reduction of Order
Lecture and applications
5. Week
Nonhomogeneous Equations; Method of Undetermined Coefficients, Variation of Parameters
Lecture and applications
6. Week
Higher-Order Linear Differential Equations; General Theory of nth Order Linear Equations; Homogeneous Equations with Constant Coefficients
Lecture and applications
7. Week
The Method of Undetermined Coefficients; The Method of Variation of Parameters
Lecture and applications - Midterm Exam
8. Week
The Laplace Transform; Definition of the Laplace Transform; Solution of Initial Value Problems
Lecture and applications
9. Week
System of First-Order Linear Equations; Review of Matrices; Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Lecture and applications
10. Week
Basic Theory of Systems of First Order Linear Equations; Homogeneous Linear Systems with Constant Coefficients; Complex Eigenvalues
Lecture and applications
11. Week
Fundamental Matrices, Repeated Eigenvalues, Nonhomogeneous Linear Systems
Lecture and applications
12. Week
Series Solution of Second-Order Linear Equations; Series Solutions Near an Ordinary Point
Lecture and applications
13. Week
Euler Equations; Regular Singular Points
Lecture and applications
14. Week
Series Solutions Near a Regular Singular Point
Lecture and applications
15. Week
Final Exam
Exam
16. Week
Final Exam
Exam
17. Week
Final Exam
Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
60
Final Exam
1
40
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems.
PO-2
Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex systemi process, device or product under realistic constraints and conditions, in such a way as to meet the desired results; ability to apply modern design methods for this purpose.
PO-4
Ability to select and use modern techniques and tools needed for analyzing and Solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectivley, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instruction.
PO-8
Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9
Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO-10
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO-11
Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
Understands the solutions of some types of differential equations and identifies the classification of differential equations.
LO-2
Express linear equations, integration factor, seperable differential equations, exact differential equation and the method of integration factor
LO-3
Understands the Eulers method and interprets the Existence and Uniqueness Theorem
LO-4
Understands the homogenuous equations with constant coefficeients and express the solutions of linear homogenuous equations by using the Wronskian.
LO-5
Describes complex roots and repeated roots of the characterictic equation and interprets the order reducing method
LO-6
Understands the non-homogenuous differential equations, the method of undetermined coefficients and the method of variation of parameters
LO-7
Understands the general theory of high-order differential equations
LO-8
Understands the series solutions near an ordinary point and applies it to Euler equations. Express regular singular points.
LO-9
Understands the series solutions near a regular singular point
LO-10
Express the Laplace transform and explains the solutions of initial value problems
LO-11
Explains the fundamental theory of first order linear differential equations, understands systems of homogenuous linear differential equations and applies comlex eigenvalues.
LO-12
Understands the fundamental matrices, repeted eigenvalues and systems of non-homogenuous linear differential equations.
